1. Field of the Invention
The present invention relates to a stepping motor.
2. Related Background Art
FIG. 1 illustrates the structure of a stator set employed in a conventional stepping motor, having pole pieces arranged around and parallel to a rotor shaft, as disclosed, for example, in the U.S. Pat. No. 3,549,918, wherein a stator set is composed of stators 1, 2 respectively having comb-shaped stator poles 1a, 2a. The stator of the stepping motor is composed of said stator set and another identical stator set, arranged back to back at the stators 2, 2'. Said stators 2, 2' are provided with circular bosses 2b, 2b' and holes 2c, 2c' in such a manner that two stator sets are displaced mutually by a 1/4 pitch.
FIG. 2 is a perspective view of a stepping motor constructed as explained above, wherein a rotor magnet 4 is coaxially fixed on a rotor shaft 3 for rotation about said shaft, and is provided, on the periphery facing the stator poles 1a, 2a, 1a', 2a', with the same number of magnetic poles as that of the stator poles in a stator set. In FIG. 1 there are provided 24 poles, N poles and S poles inclusive as in the rotor, or 12 pole pairs. Coils 5, 6 of bifilar winding are provided respectively on the stator sets.
FIG. 3 is a diagram of a driving circuit of the stepping motor, and FIG. 4 is a timing chart showing two-phase driving pulses supplied to said driving circuit.
FIG. 5A is an extended view of stator poles and rotor magnet, wherein two stator sets are represented by a (consisting of the stators 1', 2') and b (consisting of the stators 1, 2).
In the following there will be explained the stop position of the rotor when the coils are not energized and the cogging torque.
A two-pole stepping motor shown in FIG. 5D will now be taken as a model for considering the torque between a stator set a and the rotor. Said two-pole stepping motor corresponds to a pitch of the stepping motor shown in FIG. 2.
With the x- and y-axes defined as illustrated, the torque on the rotor 7 becomes zero when the center of the magnetic pole coincides with the center of the stator pole, or, at angles .theta.=0, .pi., 2.pi., . . . , n.pi..
Also at angles .theta.=.pi./2, 3.pi./2, . . . , (2n-1).pi./2 the rotor 7 receives the same torques from the left and right stators 8, 9 so that the resulting torque is again zero. Assuming a sinusoidal change, the torque can be represented by: EQU Ta=a sin 2.theta. (1)
thus varying at a period of .pi. which is a half of the period 2.pi. of the stator poles.
The equation (1) can be written, with the number p of magnetic pole pairs of the stator or rotor, as EQU Ta=a sin 2p.theta. (2) EQU By substituting p.theta.=.alpha., EQU Ta=a sin 2.alpha. (3)
The equation (2) is represented by a mechanical angle, while the equation (3) is represented by a electric angle, which will be used in the following explanation.
In FIG. 6, a curve Ta represents the cogging torque between the stator set a and the rotor. On the other hand, the torque between the stator set b and the rotor can be written, in consideration of the aberration of 1/4 pitch of the stator set b with respect to the set a, as: ##EQU1## or, for the electric angle as: ##EQU2## Thus Tb is different from Ta merely in sign.
The cogging torque To of the entire stepping motor can be represented as the sum of cogging torques working on the rotor from two stator sets a, b so that ##EQU3## A curve To in FIG. 6 shows the cogging torque in case of a.sub.1 &gt;b.sub.1. The cogging torque of the entire stepping motor is the same, in the same number and positions of the points where the torque is zero, as the torque between a single stator set and the rotor, and is different in that the peak value is smaller. The cogging torque is zero if a.sub.1 =b.sub.1, and can be set at an arbitrary magnitude if a.sub.1 and b.sub.1 are arbitrarily regulatable.
In the following there will be explained the relation between the stop position of the rotor and the positions where the cogging torque To is zero.
Between the magnetic energy W of the rotor magnet of a stepping motor and the cogging torque thereof there stands a general relation ##EQU4## so that the magnetic energy W can be represented as: ##EQU5##
FIG. 7 shows the relation between the magnetic energy mentioned above and the rotor position. The rotor 4 tends to stop at a position of minimum magnetic energy. At the positions .alpha.=.pi./2, 3.pi./2, . . . , (2n-1).pi./2 where the cogging torque is equal to zero, the rotor is unstable and does not stop due to the high magnetic energy, unless the frictional force is high. Thus the rotor eventually stops in stable manner at the positions .alpha.=0, .pi.2.pi., . . . , n.pi..
Thus the rotor stably stops where the value of the cogging torque changes from negative to positive, but it does not stop stably where said value changes from positive to negative.
As explained above, when the coils of a stepping motor are not energized, the stop positions of the rotor are .alpha.=0, .pi., 2.pi., . . . , n.pi. wherein n is an integer.
In the following there will be given an explanation on the operation of one-pitch rotation of the rotor when the coils of the stepping motor, shown in FIGS. 2 and 3, are energized as shown in FIG. 4, whlle making reference to the extended view of the stator poles and the rotor magnetic poles in FIG. 5A.
When the coils are not energized, the rotor 4 is positioned at .alpha.=0 as already explained. Then, when the phases A and B are energized, the magnetic pole 4a assumes a position at the center of or distanced by 1/8 pitch from the stator poles 1a and 1a', or .alpha.=.pi./4. At the succeeding energization of the phases B and A, the magnetic pole proceeds to a position of 3/8 pitch between 1/2-pitch and 1/4-pitch, or .alpha.=3.pi./4. Then in response to the energization of the phases A and B, it assumes a position of 5/8 pitch between 1/2-pitch and 3/4-pitch, or .alpha.=5.pi./4. Then in response to the energization of the phases B and A, it assumes a position of 7/8 pitch between 3/4-pitch and one pitch, or .alpha.=7.pi./4. Subsequently there is repeated the above-explained cycle, starting from the energization of the phases A and B.
Now reference is made to FIG. 5B for explaining the error in the stop angle of the rotor in the energized state of the coils. The upper positive half in the ordinate indicates a torque for reversing the movement of the rotor, while the lower negative half indicates a torque for assisting said movement.
The rotor is positioned at .alpha.=0 in the unenergized state.
In the first step of energization, in which the phases A and B are energized, a torque indicated by a broken line 10 is generated to advance the rotor 4 to a position .alpha.=.pi./4 where the energization torque is zero. On the other hand, at said position .alpha.=.pi./4, there exists a cogging torque (a.sub.1 -b.sub.1) for returning the rotor toward the position .alpha.=0. Consequently the rotor stops at a position where the cogging torque for returning the rotor is balanced with the rotor-advancing torque generated by the energization of the phases A and B. This stop position, .alpha.=.alpha..sub.1 shown in FIG. 5B, is in front of the proper stop position .alpha.=.pi./4. In the second step, the phases A, B are energized to generate a magnetization torque indicated by a broken line 11, acting to advance the rotor to a position .alpha.=3.pi./4 where the magnetization torque is zero.
On the other hand, at said position .alpha.=3.pi./4 there exists a cogging torque -(a.sub.1 -b.sub.1) for advancing the rotor. Consequently the rotor is stopped at a position where the advancing cogging torque is balanced with the rotor reversing torque generated by the energization of the phases A and B. This stop position, .alpha.=.alpha..sub.2 shown in FIG. 5B, is beyond the proper stop position .alpha.=3.pi./4.
The process in the succeeding third step is same as that in the first step, whereby the rotor stops at a position .alpha..sub.3 in front of the proper stop position .alpha.=5.pi./4. The process in the fourth step is same as that in the second step, whereby the rotor stops at a position .alpha..sub.4 beyond the proper stop position .alpha.=7.pi./4. FIG. 5D shows the angular error of rotor position with respect to the proper stop position in ordinate and the number of steps of the stepping motor in abscissa. In the two-phase driving process the angular error of the rotor position changes its sign at every step, showing an excessive movement and a deficient movement alternatively. In this manner it has not been possible to achieve a uniform and exact movement.